Noise appears locked to the camera, as if looking trough a dirty glass
On the sampling section enable the icon that looks like a clock.
That will generate a different seed for every frame, making the noise pattern different.

Blatantly taken form the Blender Manual:

Seed
Seed value for integrator to get different noise patterns.
Animate Seed (clock icon)
This button which can be found on the right side of the Seed value can be used to give different seed values. It is a good idea to enable this when making animation because in the real world each frame has a different noise pattern.